Lampedusa and Linosa, together known as the Pelagie Islands, are famous for some of the clearest water anywhere in the Mediterranean, closer to the coast of Tunisia than to mainland Sicily. Despite that distance, they're more reachable from Agrigento than most visitors realise.
The only departure port for both islands is Porto Empedocle, a short drive from Agrigento's old town, the same working port where Inspector Montalbano was filmed. Two ferry companies run the route: Liberty Lines operates a fast hydrofoil in the summer season only, taking around 4 hours 15 minutes, while Siremar runs a larger, more traditional ferry year-round, taking roughly 9 to 10 hours but carrying vehicles.
Lampedusa itself has some of the best beaches in Italy, most famously the Rabbit Beach (Spiaggia dei Conigli), regularly ranked among the best beaches in the world. Linosa, smaller and quieter, is known for its black volcanic sand and a more low-key pace.
Photos via Wikimedia Commons